Extant wind-turbines are based on the aerodynamic principles of a wing. The turbine is equipped with wing-shaped turbine blades. As wind blows across the wing-shaped turbine blades, pressure differences generated on either side of the blades, in accordance with Bernoulli's Law, create aerodynamic force, or lift. This induces the blades to rotate, and the rotation drives an electric generator.
The maximum efficiency, according to Betz's law, that a bladed wind turbine can achieve is approximately 59.3%. This has long been considered an absolute limiting function with respect to use of the wind to generate usable energy.
This wind to power extraction available for bladed wind turbines is expressed by the following equation:P=ρAv3 where ρ is the power in watts, p is the density of air, A is the cross sectional area swept by the blades, and v is the velocity of the wind.
One may easily surmise, then, that the bladed turbine engineer's only practical means of increasing the power output of a given bladed wind turbine design is to increase the swept area of the blades. This produces an only a linear, or one to one, increase in power output, swept-area unit per power-unit.
However, again referring to the equation, if flow velocity could be increased, a disproportionate benefit would be derived. For example, a mere 50 percent increase in flow velocity would quadruple the theoretical power output. A number of turbine designers, in pursuit of this disproportionate benefit, have attempted to exceed the Betz limit by exploiting the venture effect of a shroud or casing so configured as to act as a giant nozzle surrounding essentially conventional turbine blades to increase the wind-velocity impinging upon them. The blades in such designs, however, remain as a limiting factor.
In contrast, the herein taught invention uses a novel approach to this energy translation problem. It substitutes convergent/divergent, or venturi, nozzles, resembling those such as would be employed by rockets, in place of turbine blades and thereby provides a means by which wind velocity through the device may be amplified. The convergence/divergence as embodied herein may be contained entirely within the nozzle, or may be manifested by convergence of conduit guided fluid flow which diverges only at ejection. But in either case, amplifying this flow-velocity, and commensurately, the ejection velocity at the nozzle, a significant increase in output energy is realized. The increase in output energy, as expressed by the above equation, is not a linier function, but is, rather, a function of the cube of the nozzle ejection velocity increase.
If we compare this method of increasing energy output by using nozzles to increase ejection velocity, to the method of increasing output by increasing the blades swept area, the advantage is clear. The ratio of increase based on blade swept area is merely 1 to 1. The increase based on increased ejection velocity, however, is a cubic function, the output energy increasing as a cube of the nozzle ejection velocity.
By exploiting the advantage of the velocity to power function, this invention is able to essentially circumvent the limitations of Betz's law by eliminating the employment of precisely the physical components (turbine blades) to which Betz's Law applies.
A computational computer model using popular, commercially available three-dimensional and computational fluid dynamics, or CFD, software, was developed for this aeolipile invention to obtain torque production formula, derive efficiency limits, and to demonstrate practicality. Simulations were conducted for a single thrust nozzle to establish flow parameters. For these simulations, an inlet velocity of 2 m/sec was chosen. After 1600 iterations, the corresponding outlet velocity was found to be near 17 m/sec, a flow velocity increase of 15 m/sec, thereby validating the inventions theoretical functionality.
Tests were also conducted with respect to an expanded wind-gathering configuration of a horn-shaped inlet extension as in FIG. 7, below. Test employed inlet airflow velocities of 2, 4, 6, 8, 10, and 12 m/sec and were repeated for various inlet/outlet size ratios. FIG. 8, below plots the flow velocity increases, produced for each inlet/outlet size ratio.